Advanced General Relativity : Gravity Waves, Spinning Particles, and Black Holes

[BOOK DESCRIPTION]

This book is aimed at students making the transition from a first course on general relativity to a specialized subfield. It presents a variety of topics under the general headings of gravitational waves in vacuo and in a cosmological setting, equations of motion, and black holes, all having a clear physical relevance and a strong emphasis on space-time geometry. Each chapter could be used as a basis for an early postgraduate project for those who are exploring avenues into research in general relativity and who have already accumulated the required technical knowledge. The presentation of each chapter is research monograph style, rather than text book style, in order to impress on interested students the need to present their research in a clear and concise format. Students with advanced preparation in general relativity theory might find a treasure trove here.

[TABLE OF CONTENTS]

 1 Minkowskian space-time                       1  (9)
      1.1 Lorentz tansformations                   1  (2)
      1.2 Non-singular and singular Lorentz        3  (3)
      transformations
      1.3 Infinitesimal Lorentz transformations    6  (2)
      1.4 Geometrical construction of a            8  (2)
      gravitational wave
    2 Plane gravitational waves                    10 (18)
      2.1 From linear approximation to             10 (7)
      colliding waves
      2.2 Electromagnetic shock waves              17 (4)
      2.3 Gravitational shock waves                21 (3)
      2.4 High-frequency gravity waves             24 (4)
    3 Equations of motion                          28 (28)
      3.1 Motivation                               28 (5)
      3.2 Example of a background space-time       33 (4)
      3.3 Equations of motion of a                 37 (2)
      Reissner-Nordstrom particle in first
      approximation
      3.4 Background space-time for a Kerr         39 (6)
      particle
      3.5 Equations of motion of a Kerr            45 (8)
      particle in first approximation
      3.6 Spinning test particles                  53 (3)
    4 Inhomogeneous aspects of cosmology           56 (23)
      4.1 Plane-fronted gravitational waves        56 (4)
      with a cosmological constant
      4.2 Perturbations of isotropic cosmologies   60 (4)
      4.3 Gravitational waves                      64 (9)
      4.4 Cosmic background radiation              73 (6)
    5 Black holes                                  79 (39)
      5.1 Introduction: Basic properties of        79 (7)
      black holes
      5.2 Collapsing null shells and trapped       86 (5)
      surface formation
      5.3 Scattering properties of high-speed      91 (12)
      Kerr black holes
      5.4 Inside the black hole                    103(7)
      5.5 Metric fluctuations and Hawking          110(8)
      radiation
    6 Higher dimensional black holes               118(13)
      6.1 Brief outline of D-dimensional black     119(3)
      holes
      6.2 Gibbons-Penrose isoperimetric            122(2)
      inequality and the hoop conjecture in D
      dimensions
      6.3 Light-like boost of higher               124(7)
      dimensional black holes
Appendix A Notation                                131(2)
Appendix B Transport law for k along r = 0         133(2)
Appendix C Some useful scalar products             135(2)
References                                         137(5)
Index                                              142